A research program for direct numerical simulations of compressible reacting flows is described. Two main research subjects are proposed: the effect of pressure waves on turbulent combustion and the use of direct simulation methods to validate flamelet models for turbulent combustion. The interest of a compressible code to study turbulent combustion is emphasized through examples of reacting shear layer and combustion instabilities studies. The choice of experimental data to compare with direct simulation results is discussed. A tentative program is given and the computation cases to use are described as well as the code validation runs.